不确定微分方程的数值解法及其应用研究  

The Numerical Solution of the Uncertain Differential Equation and Its Application

作　　者：王志刚 申康 王思哲 WANG Zhi-gang;SHEN Kang;WANG Si-zhe(School of Science,Hainan University,Haikou 570228,China;School of Automation,Central South University,Changsha 410083,China)

机构地区：[1]海南大学理学院,海南海口570228 [2]中南大学自动化学院,湖南长沙410083

出　　处：《模糊系统与数学》2020年第1期141-148,共8页Fuzzy Systems and Mathematics

基　　金：海南省自然科学基金高层次人才项目(2019RC168);海南省科协青年科技英才创新计划项目(QCXM201806)。

摘　　要：不确定微分方程广泛应用于不确定财政、不确定控制、不确定微分博弈等领域。由于一些不确定微分方程解析解难以实现,本文首先研究了不确定微分方程的Euler方法和Runge-Kutta方法两种数值解法,并进行误差分析。通过比较随机领域Black-Scholes模型和不确定领域Liu模型的欧式期权定价公式,验证不确定微分方程描述证券市场的合理性和实用性。Uncertain differential equations are widely used in uncertain finance, uncertain control, uncertain differential game and so on. It is difficult to find the analytical solution of some uncertain differential equations. In this paper, two numerical solutions of uncertain differential equations, Euler method and Runge-Kutta method are studied firstly, and the errors analysis are carried out. By comparing the European option pricing formulas of the stochastic domain Black-Scholes models and the uncertain domain Liu models, the rationality and practicability of the uncertain differential equations for describing the stock market are verified.

关 键 词：不确定理论 不确定微分方程 EULER方法 RUNGE-KUTTA方法 期权定价公式 

分 类 号：O211[理学—概率论与数理统计]